1. Field of the Invention
This invention relates to a codifying and storing method for fuzzy membership functions, the membership degree, as well as to a corresponding circuit for calculating the membership degree.
Specifically, the invention relates to a codifying and storing method for membership functions representing a membership degree of fuzzy variables defined within a universe of discourse which is discretized into a finite number of points.
The invention also relates to a method for calculating the value of the membership degree of a fuzzy variable defined within a universe of discourse which is discretized into a finite number of points with reference to a membership function thereof.
The invention further relates to a circuit for calculating the membership degree of a fuzzy variable within a universe of discourse which is discretized into a finite number of points with reference to a membership function thereof.
2. Description of the Related Art
As is well known, a membership function (hereinafter also MF) is a single-variable function which, therefore, can be represented on a two-dimensional graph.
In particular, such a function represents the membership degree, MF(x), of a fuzzy variable x, and can be reproduced on a graph having the fuzzy variable x plotted on one axis and the respective membership degree, commonly designated α, plotted on the other axis.
The codifying of the membership functions MF has been the subject of extensive investigations, due to the fact that it takes up a considerable amount of memory when the membership functions MF need to be stored, for instance, in a possible calculating structure.
In particular, with a digital calculating structure, a necessary simplification is that of discretizing the membership functions MF as integer values of the fuzzy variable x in a so-called “universe of discourse” (U.d.D.). Each membership function MF is then defined by 0 to 2n−1 points, i.e., discretized into n bits.
Several techniques for storing membership functions MF are known.
A first known storing method uses a table for storing up, point by point, the value of the membership function MF, meaning that, for each discretized value of the fuzzy variable x, a corresponding membership degree α is stored.
This first known method has a major advantage in that membership functions MF of any forms can be stored, and that the membership degrees α can be extracted at a fast rate starting from a given fuzzy variable x.
However, this approach has an important drawback in that the punctual storing of all the membership functions MF takes up a considerable amount of memory.
Also known is to reduce the set of representable membership functions MF down to a sub-set which contains only certain geometric figures and, within this constraint, to use parameters for storing the membership functions MF. In particular, based on these parameters, the membership degree α of a membership function MF can be calculated as a function of the fuzzy variable x, thereby saving much memory area.
There is also a dramatic decrease in the membership functions MF that can be represented with any accuracy, that is readily reduced to the allowable sub-set of geometric figures.
This prior codifying and storing method for membership functions MF is used, for example, in U.S. Pat. No. 5,875,438, filed on Feb. 23, 1999.
Furthermore, this type of an approach requires complicated dedicated hardware for calculating the membership degree α from a given fuzzy variable x, and takes a long time to calculate the corresponding membership degrees α.
The technical problem underlying this invention is to provide a storing method for membership functions MF which would apply to functions of any forms, while occupying but a small amount of memory area, so as to overcome the limitations of known storing methods.